Sumati wanted to see the stars of the night sky. She knows that she needs a telescope to see those distant stars. She finds out that the telescopes, which are made of lenses, are called refracting telescopes and the ones which are made of mirrors are called reflecting telescopes.

So she decided to make a refracting telescope. She bought two lenses, `L_(1)` and `L_(2)`. out of which `L_(1)` was bigger and `L_(2)` was smaller. The larger lens gathers and bends the light, while the smaller lens magnifies the image. Big, thick lenses are more powerful. So to see far away, she needed a big powerful lens.Unfortunately, she realized that a big lens is very heavy. Heavy lenses are hard to make and difficult to hold in the right place. Also since the light is passing through the lens, the surface of the lens has to be extremely smooth. Any flaws in the lens will change the image. It would be like looking through a dirty window.
If the powers of the lenses `L_(1)` and `L_(2)` are in the ratio of `4:1`, what would be the ratio of the focal length of `L_(1)` and `L_(2)`

Options

A. `4:1`
B. `1:4`
C. `2:1`
D. `1:2`

Explanation

`P=1//f`
`P_(1)/f_(1)` and `P_(2)=1//f_(2)`
`P_(1)//P_(2)=4`, hence `(1\\f_(1))//1\\f_(2))=4//1`
Hence `f_(1)//f_(2)=1//4`
b) `1//4`